_{m}) and mixture friction factor (f

_{m}) terms ...

The formula for calculating the pressure drop for two-phase fluids in pipes is analogous to the equivalent single-phase flow version shown in Eqn (3.19), except that the friction factor and physical properties are replaced by their two-phase equivalents:

$-\frac{dP}{dL}=\frac{g}{{g}_{\text{c}}}{\rho}_{\text{M}}\mathrm{sin}\theta +\frac{{f}_{\text{M}}{\rho}_{\text{M}}{v}_{\text{M}}^{2}}{2{g}_{\text{c}}{d}_{\text{i}}}+\frac{{\rho}_{\text{M}}{v}_{\text{M}}d{v}_{\text{M}}}{{g}_{\text{c}}{d}_{\text{L}}}$

(3.68)

The pressure loss term in Eqn (3.34) includes a two-phase friction factor, f_{M}. In the past, researchers have spent much effort in developing predictive correlations for the two-phase friction factor, as well as the slip liquid holdup term.

Definitions of the mixture density (ρ_{m}) and mixture friction factor (f_{m}) terms ...

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